{"paper":{"title":"Finite size corrections at the hard edge for the Laguerre $\\beta$ ensemble","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Allan K. Trinh, Peter J. Forrester","submitted_at":"2019-03-21T03:44:58Z","abstract_excerpt":"A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre $\\beta$ ensemble, characterised by the Dyson parameter $\\beta$, and the Laguerre weight $x^a e^{-\\beta x/2}$, $x > 0$ in the hard edge limit. The latter relates to the eigenvalues in the vicinity of the origin in the scaled variable $x \\mapsto x/4N$. Previous work has established the corresponding functional form of various statistical quantities --- for example the distribution of the smallest eigenvalue, provided that $a \\in \\mathbb Z_{\\ge "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08823","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}